CN101800618A - LDPC code constructing method based on coding cooperative communication - Google Patents

Abstract

The invention discloses an LDPC code constructing method based on coding cooperative communication; the method comprises the following steps: 1. choose a basis matrix W (1) based on finite field multiplicative inverse; the multiplicative inverse of a certain element in the basis matrix is multiplied with each row of the basis matrix, so as to generate a multiplicative identity in the basis matrix; 3.the basis matrix is expanded, so as to obtain an expansion matrix containing diagonal line; 4. the submatrix above the diagonal line is substituted by zero matrix, so as to obtain a quasi-cyclic matrix which is provided with a lower triangular type and has a nested structure; the invention can flexibly construct the quasi-cyclic matrix with the nested structure, which is suitable for CC proposal, while reducing the code construction complexity, the complexity of a coder of a trunk node and a destination node is reduced; in addition, the code in the invention does not have short link characteristic, and the performance of the code is promoted obviously compared with the traditional decode and forward, DF proposal.

Description

A kind of LDPC code constructing method based on coding cooperative communication

Technical field

A kind of LDPC code constructing method based on coding cooperative belongs to communication channel coding and decoding field, is specifically related to the check matrix building method of the LDPC sign indicating number in the coding cooperative communication.

Technical background

Wireless system of future generation not only will improve data rate in order to satisfy the requirement of many speed multimedia communication, also will make system can guarantee the desired service quality of different medium.And the multipath fading in the radio communication is the key factor that influences communications speed and reliability, and how solving the influence that multipath effect brings is the key that improves communication quality.Adopt multiple-input and multiple-output (MIMO) technology can utilize spatial reuse to gain and improve channel capacity, can utilize again simultaneously space diversity gain effectively eliminates the wireless channel multipath, the time become the influence of decline, the reliability that the raising signal transmits.But because terminal is generally single antenna, size of wireless devices and hardware complexity have just limited the development of MIMO technology like this.Cooperative diversity technique had been proposed afterwards, promptly the single antenna user under multi-user environment is in the own data message of transmission, also can transmit the information of its reception and detected collaborative user (being the companion), constitute virtual MIMO, become the research focus of wireless communication field.

Collaborative trunking plan mainly contains forward direction and amplifies AF, decode forward DF and three kinds of schemes of coding cooperation CC.Wherein, the AF scheme is the signal that via node directly amplifies and forwarding is received from source node; The DF scheme is that via node is deciphered to the received signal, and the regeneration symbolic information of transmitting after the decoding gives destination node, more than both all belong to repeated encoding, it is very little to obtain coding gain.The CC scheme is at first to be proposed by scholars such as Hunter, is synergistic signal is combined with chnnel coding, by recompile behind the correct decoding buddy information and send, obtains diversity and coding gain simultaneously, and is therefore more excellent than AF scheme and DF scheme performance.

Low density parity check code (LDPC) is a kind of error correcting code of excellent performance, encode with LDPC and to carry out coding cooperative communication, can be under the situation of not obvious increase system bandwidth and transmitted power, utilize LDPC to be coded in performance advantage on the error correcting capability, can obtain considerable diversity gain, elevator system performance effectively, and the cost of system equipment and complexity do not have tangible increase.

For the LDPC sign indicating number, the code word that designs for single-link and design for collaboration communication is different, and it is that in collaboration communication a code word often will be divided into twice and be transferred to destination node.If successfully decoded at via node, what then destination node received is a complete code word, needs to design complete check matrix so and guarantees that the destination node reception has enough good performance.If the via node decoding failure, destination node need be deciphered the part code word, and the part code word that needs so to transmit also will have good performance.Generally speaking, both need the good performance of complete code, also needed the outstanding performance of part code word.

In order to achieve the above object, A.Chakrabarti etc. have proposed a kind of check matrix at the coding cooperative communication pattern, and its architectural feature as shown in Figure 1.Wherein, R is the matrix code check, N ₁Be the length of part code word, N is total code length, H ₁₁Be check matrix, realized the nested structure of part code word and complete code decoding like this, can realize two kinds of decoded modes with same decoder at the part codeword decoding.In addition, in order to allow two kinds of coded systems also can realize that need encoder also to have nested structure, this just requires global matrix H and matrix H with the one and same coding device ₁₁It all is the check matrix of full rank and system form.Therefore, make total check matrix have the mode of following triangle, as shown in Figure 2, can guarantee matrix H and matrix H like this ₁₁It all is the check matrix of full rank and system form.

Yet, because in the existing expansion algorithm, the check matrix of part code word and expansion square formation all are to adopt PEG structure or IPEG structure, in order to produce this nested structure, H ₁₁When being extended to H, as shown in Figure 2, there is a unit matrix expansion square formation in matrix lower right corner below; The lower left corner is the combination of fully sparse unit matrix.So just have a subject matter, add the possibility that unit matrix does not consider to form becate in the sparse zone in the lower left corner, especially length is 4 ring, and this may cause bigger influence to the performance of matrix.At the problems referred to above, the present invention proposes a kind of LDPC code constructing method based on coding cooperative, can avoid the appearance of becate, can guarantee the nested structure of matrix again, and in emulation of the present invention, adopt traditional DF scheme of Mackay random code to contrast, the performance advantage that the code word of constructing with the used algebraic method of outstanding the present invention is had in collaboration communication.

Summary of the invention

The present invention adopts in existing coding cooperative on the basis of the LDPC code check matrix with nested structure, grows and sends out from avoiding producing minimum ring, has proposed a kind of building method of the quasi-cyclic LDPC code with nested structure based on coding cooperative.The sharpest edges that this method is compared with existing LDPC code constructing method with nested structure are exactly can avoid becate to occur by the check matrix that the accurate cycle basis matrix based on finite field expands.

It is that 6 these basic principles make the quasi-cyclic LDPC code with nested structure that constructs can avoid becate (especially 4 rings) to occur automatically that this method has been utilized the minimum ring length based on the quasi-cyclic LDPC code of finite field multiplier inverse element structure, and concrete principle is proved in the back.

The specific implementation step of this method is as follows:

The first step is selected the basic matrix W based on finite field gf (q) multiplicative inverse ⁽¹⁾, wherein q is 2 power, α is the primitive element of GF (q).

$W^{\left(1\right)}=\left[\begin{array}{c}{w}_0^{\left(1\right)}\\ w_1^{\left(1\right)}\\ .\\ .\\ .\\ w_{q-2}^{\left(1\right)}\end{array}\right]$

Second goes on foot each row that removes to take advantage of basic matrix with the multiplicative inverse of the some elements in the basic matrix, because basic matrix W ⁽¹⁾Cyclic shift characteristic itself, promptly each provisional capital in the matrix is the cyclic shift of lastrow, makes that each row all multiplicative identity can occur in the basic matrix.

The 3rd step with the second step gained basic matrix expand H ⁽¹⁾,, have " diagonal " that becomes by each subsection formation after the therefore whole basic matrix expansion because the matrix of identical element expansion is a unit matrix.

The 4th step all replaced the submatrix of diagonal top with null matrix, promptly obtain the accurate circular matrix H of the following triangular form with nested structure as shown in Figure 1, was of a size of (q-1) ²* (q-1) ²

Utilize the characteristic that to avoid becate based on the multiplicative inverse basic matrix of finite field when the key of this method is choosing of first step basic matrix, and second step obtained diagonal structure by the multiplicative inverse that multiply by a certain element in the basic matrix.The minimum ring length of the last check matrix H that this method constructs is at least 6, below this conclusion of proof.

Proof: because H is at H ⁽¹⁾The basis on substitute some submatrix and obtain with null matrix, only need proof H ⁽¹⁾Minimum ring length is 6, and promptly the minimum ring length of provable H is 6.

Suppose H ⁽¹⁾Having length is 4 ring, must have integer k so, l, and m, n, 0≤k wherein, l, m, n＜q-1 and m ≠ n make vectorial α ^kw _mAnd α ^lw _nThere are two positions that identical element is arranged.Make s, t (0≤s, t＜q-1, s ≠ t) represent this two positions, then we can obtain following equation:

α ^k(α ^mα ^s+(α ^mα ^s) ^-1)＝α ^l(α ⁿα ^s+(α ⁿα ^s) ^-1)

α ^k(α ^mα ^t+(α ^mα ^t) ^-1)＝α ^l(α ⁿα ^t+(α ⁿα ^t) ^-1)

By following formula, we can obtain (α ^T-s-α ^S-t) (α ^N-m-α ^M-n)=0, thereby α as can be known ^T-s=α ^S-tAnd α ^N-m=α ^M-nAn establishment must be arranged.If α ^T-s=α ^S-t, we can get 2 (t-s)=c (q-1), and wherein c is an integer.Notice 0≤s, t＜q-1, and q-1 can not be divided exactly by 2, so c=0, t=s then, this contradicts with the fact of before s ≠ t.In like manner, α ^N-m=α ^M-nCan release with the fact of m ≠ n and contradict, therefore hypothesis is false, so H ⁽¹⁾Minimum ring length be 6, i.e. proposition is set up.

In the coding cooperative communication that adopts code word of the present invention, first time slot, source node is with the part matrix H among the present invention ₁₁Pairing bit is broadcast to via node and destination node, if via node can correct decoding, then the pairing bit of matrix H remainder is sent to destination node; Otherwise, do not send.Second time slot, destination node is deciphered according to the decoding situation of via node.If via node is successfully decoded, then destination node uses complete matrix H and deciphers; Otherwise, use part matrix H ₁₁Decipher.Like this, for via node and destination node, only need to use same coder to get final product, thereby reduced the complexity of the coding and decoding of whole system.

In sum, code word building method that the present invention proposes and embodiment mainly contain following characteristics and are: the one, and the code word of the present invention circular matrix that is as the criterion can expand by basic matrix, therefore greatly reduces the complexity of code word structure; The 2nd, the accurate circular matrix with nested structure that the present invention constructed can be avoided becate automatically, makes the performance of code word coder be significantly improved; The 3rd, in coding cooperative communication, nested structure of the present invention makes via node and destination node only need use same coder to get final product, thereby has reduced the hardware complexity at the node place.

Description of drawings:

Fig. 1 is the check matrix with LDPC sign indicating number of nested structure.

Fig. 2 is the following triangle check matrix example of nested structure.

Fig. 3 is the QC-LDPC sign indicating number that has nested structure in the example 1.

Fig. 4 is the CC scheme that adopts (3024,1323) sign indicating number that the present invention constructed and the re-transmission ratio of Mackay random code (1512,1323) is 0.75 DF scheme comparison.

Fig. 5 adopts CC scheme of (3024,1323) sign indicating number that the present invention constructed and the DF scheme comparison that Mackay random code (1512,1323) retransmits fully.

Embodiment:

Below in conjunction with an example application of the present invention is described in detail, and provided simulation result.

Example 1

The first step is selected finite field gf (2 ⁶) on multiplicative inverse basic matrix W ⁽¹⁾

Second step, therefore the transposing by row matrix was placed on identical element on the basic matrix diagonal owing to multiplicative identity occurred in this basic matrix;

The matrix that obtains during the 3rd step went on foot second is at GF (2 ⁶) expand on the territory extended matrix H ⁽¹⁾, H ⁽¹⁾One " diagonal " appears in middle meeting;

The 4th step was got H ⁽¹⁾1323 * 3024 the matrix in the upper left corner, and the submatrix above the diagonal substituted with null matrix, the QC-LDPC sign indicating number that triangular form has (3024,1323) of nested structure promptly obtained down, as shown in Figure 3.

The LDPC code word that above-mentioned steps constructed is applied in the CC scheme, first time slot, source node is with part matrix in the matrix

Pairing bit is broadcast to via node and destination node, and via node is deciphered, if decoding is correct, then sends remaining bits to destination node; Otherwise, do not send bit.Second time slot, destination node is deciphered situation according to via node, selects to use part matrix Or H _{1323 * 3024}Decipher.

Fig. 4 and Fig. 5 have provided respectively under the situation that part retransmits and retransmits fully, the performance that adopts CC scheme that the present invention designs code word and traditional DF scheme of Mackay random code relatively wherein is meant that for the re-transmission of employing CC scheme of the present invention bit that second time slot via node passed accounts for the percentage of bit that source node sends in first time slot.From simulation result as can be seen, under the situation that part retransmits, adopt (2646,1323) sign indicating number and Mackay random code (1512 of the upper left side correspondence in the check matrix of the present invention, 1323) re-transmission ratio is that 0.75 DF scheme is compared, and can obtain the performance gain of 0.5dB.Under situation about retransmitting fully, based on the performance gain of nearly 1.5 dB of CC scheme of the present invention.In addition, this performance advantage can be all the more obvious along with the increase of the ratio of re-transmission.

Claims (7)

1. LDPC code constructing method based on coding cooperative, its feature may further comprise the steps:

The first step is selected the basic matrix W based on the finite field multiplier inverse element ⁽¹⁾

Second step went to take advantage of each of basic matrix capable with the multiplicative inverse of the some elements in the basic matrix, made multiplicative identity to occur in the basic matrix;

The 3rd step obtained comprising cornerwise extended matrix H with the basic matrix expansion ⁽¹⁾

The 4th step all replaced the submatrix of diagonal top with null matrix, promptly obtain down the accurate circular matrix of triangular form;

2. as right 1 said a kind of LDPC code constructing method, it is characterized in that based on coding cooperative: the selected basic matrix of this method based on the finite field multiplier inverse element, get the basic matrix of its each element, the check matrix H that obtains through expansion as the index gained ⁽¹⁾Have accurate circulation form, each provisional capital is the cyclic shift of lastrow, and its minimum ring length is 6;

3. as right 1 said a kind of LDPC code constructing method based on coding cooperative, it is characterized in that: the element chosen is the some elements in the element set in the basic matrix in described second step, and each row of the multiplicative inverse of selected element and basic matrix is multiplied each other, and an index is arranged is 0 element for back each provisional capital of gained matrix;

4. as right 1 said a kind of LDPC code constructing method based on coding cooperative, it is characterized in that: described the 3rd step after expansion, can occur containing cornerwise extended matrix with second basic matrix that goes on foot acquisition;

5. as right 1 said a kind of LDPC code constructing method based on coding cooperative, it is characterized in that: at the accurate circular matrix of following triangular form of described the 4th step gained, because its nested structure, can regard as by four sub-matrixes and form, upper left submatrix is the submatrix with accurate loop structure, upper right submatrix is a null matrix, and the lower-left submatrix also is the submatrix with accurate loop structure, and the bottom right submatrix is the circular matrix of following triangular form;

6. as right 1 said a kind of LDPC code constructing method based on coding cooperative, it is characterized in that: in coding cooperative communication, source node sends the upper left submatrix in this method, if via node decoding is correct, then via node sends remaining code word in the re-transmission ratio, otherwise via node does not send code word, and destination node only need use same decoder can handle above two kinds of situations;

7. as right 1 said a kind of LDPC code constructing method based on coding cooperative, it is characterized in that: adopt the CC scheme of the sign indicating number of the present invention's structure to compare with the traditional DF scheme that adopts the Mackay random code, performance increases along with the re-transmission ratio and obvious gain is arranged, and the LDPC sign indicating number that has demonstrated fully algebraically building method structure in collaboration communication is compared the advantage on the performance with random code.

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